This paper introduces the averaging principle (AP) as a method for solving fuzzy stochastic fractional integro-evolution equations (FSFIEEs). By making certain assumptions, the solutions of FSFIEEs can be estimated as mean square solutions of averaged fuzzy stochastic systems. This technique simplifies the analysis and comprehension of complex systems that are subject to both randomness and uncertainty.
{"title":"Approximating solutions of fuzzy stochastic fractional integro-evolution equations with the Averaging Principle: Theory and Applications","authors":"Hafiza Maria Arshad, Ramsha Shafqat","doi":"10.52223/ijam.20222204","DOIUrl":"https://doi.org/10.52223/ijam.20222204","url":null,"abstract":"This paper introduces the averaging principle (AP) as a method for solving fuzzy stochastic fractional integro-evolution equations (FSFIEEs). By making certain assumptions, the solutions of FSFIEEs can be estimated as mean square solutions of averaged fuzzy stochastic systems. This technique simplifies the analysis and comprehension of complex systems that are subject to both randomness and uncertainty.","PeriodicalId":338406,"journal":{"name":"International Journal of Advancements in Mathematics","volume":"458 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117014678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we are going to study the numerical investigation of oblique stagnation point flow of Casson-nano fluids along with convective boundary conditions. Mixed boundary conditions for active and passive control are also number, and presents the findings using tables and graphs. The study reveals that an increase in the Biot number and thermal radiation parameter results in an enhancement of the temperature distribution, while an increase in the suction/injection parameter causes a reduction in the velocity and temperature distributions for both injection and suction cases.
{"title":"Numerical Investigation of Active and Passive Control of MHD Oblique Stagnation Point Flow of Casson-Nano Fluid Along with Convective Boundary Conditions","authors":"","doi":"10.52223/ijam.20222205","DOIUrl":"https://doi.org/10.52223/ijam.20222205","url":null,"abstract":"In this paper, we are going to study the numerical investigation of oblique stagnation point flow of Casson-nano fluids along with convective boundary conditions. Mixed boundary conditions for active and passive control are also number, and presents the findings using tables and graphs. The study reveals that an increase in the Biot number and thermal radiation parameter results in an enhancement of the temperature distribution, while an increase in the suction/injection parameter causes a reduction in the velocity and temperature distributions for both injection and suction cases.","PeriodicalId":338406,"journal":{"name":"International Journal of Advancements in Mathematics","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133818251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hafiza Maria Arshad, Syed Zargham Haider Sherazi, Mehwish Iqbal, M. U. Mehmood
This work present the controllability of fractional evolution equations of order (1, 2).We use the fractional calculus, the Monch fixed point (MFP) theorem and measure of non-compactness (MNC). A controllability result is given out for the nonlocal Cauchy problem of the fractional evolution equations including noncompact semigroups (NCSG) and the functions by excluding Lipschitz continuity. The associated theorems and properties are demonstrated in detail and an example is stated to clarify the effectiveness of the theoretical outcomes.
{"title":"Non-Compact Semigroups and Controllability of Fractional Evolution Equations of Order (1, 2)","authors":"Hafiza Maria Arshad, Syed Zargham Haider Sherazi, Mehwish Iqbal, M. U. Mehmood","doi":"10.52223/ijam.20222201","DOIUrl":"https://doi.org/10.52223/ijam.20222201","url":null,"abstract":"This work present the controllability of fractional evolution equations of order (1, 2).We use the fractional calculus, the Monch fixed point (MFP) theorem and measure of non-compactness (MNC). A controllability result is given out for the nonlocal Cauchy problem of the fractional evolution equations including noncompact semigroups (NCSG) and the functions by excluding Lipschitz continuity. The associated theorems and properties are demonstrated in detail and an example is stated to clarify the effectiveness of the theoretical outcomes.","PeriodicalId":338406,"journal":{"name":"International Journal of Advancements in Mathematics","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132865981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. U. Mehmood, Syed Zargham Haider Sherazi, Mehwish Iqbal
In this paper, we will examine the facts in the image of infinite time delay on the mild solution’s solvability and fractional integro-differential Evolution Equation of Banach space’s optimal control choosing order ? ? (1,2). For investigation of mild solution of the system, continuation, uniqueness and the existence of the solution with the help of grown-wall inequality will be discussed shortly. After constructing the lagrange problem, the demonstration of actuality of optimal control of fractional integro delay system is being proceed. And at the end we will discuss the regarding result by an adequate example.
{"title":"Optimal Control of Fractional Integro-differential Evolution Equation with Infinite Delay of order (1; 2)","authors":"M. U. Mehmood, Syed Zargham Haider Sherazi, Mehwish Iqbal","doi":"10.52223/ijam.20222203","DOIUrl":"https://doi.org/10.52223/ijam.20222203","url":null,"abstract":"In this paper, we will examine the facts in the image of infinite time delay on the mild solution’s solvability and fractional integro-differential Evolution Equation of Banach space’s optimal control choosing order ? ? (1,2). For investigation of mild solution of the system, continuation, uniqueness and the existence of the solution with the help of grown-wall inequality will be discussed shortly. After constructing the lagrange problem, the demonstration of actuality of optimal control of fractional integro delay system is being proceed. And at the end we will discuss the regarding result by an adequate example.","PeriodicalId":338406,"journal":{"name":"International Journal of Advancements in Mathematics","volume":"223 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114680411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The article examines the characteristics of heat transfer for steady two-dimensional MHD Casson fluid with shear thickening properties in the presence of variable heat source for a vertical stretching sheet. The study considers the thermal radiation’s impact and velocity slip, and uses similarity transformations to convert the governing PDEs and corresponding boundary conditions into ODEs. Numerical solutions are obtained using shooting and R. K-4 methods, and the results presented for both injection and suction cases. The article examines the influence of various neutral parameters on the distribution of temperature, skin friction coefficient, velocity, and local Nusselt number, and presents the findings using tables and graphs. The study reveals that an increase in the Biot number and thermal radiation parameter results in an enhancement of the temperature distribution, while an increase in the suction/injection parameter causes a reduction in the velocity and temperature distributions for both injection and suction cases.
{"title":"Numerical Investigation of Suction/Injuction on Triple Diffusive MHD Casson Fluid Flow over a Vertical Stretching Surface","authors":"H. Irfan, Anum Khan","doi":"10.52223/ijam.20222202","DOIUrl":"https://doi.org/10.52223/ijam.20222202","url":null,"abstract":"The article examines the characteristics of heat transfer for steady two-dimensional MHD Casson fluid with shear thickening properties in the presence of variable heat source for a vertical stretching sheet. The study considers the thermal radiation’s impact and velocity slip, and uses similarity transformations to convert the governing PDEs and corresponding boundary conditions into ODEs. Numerical solutions are obtained using shooting and R. K-4 methods, and the results presented for both injection and suction cases. The article examines the influence of various neutral parameters on the distribution of temperature, skin friction coefficient, velocity, and local Nusselt number, and presents the findings using tables and graphs. The study reveals that an increase in the Biot number and thermal radiation parameter results in an enhancement of the temperature distribution, while an increase in the suction/injection parameter causes a reduction in the velocity and temperature distributions for both injection and suction cases.","PeriodicalId":338406,"journal":{"name":"International Journal of Advancements in Mathematics","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114421680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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